Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique

We present a Master equation for description of fermions and bosons for special relativities with two invariant scales, SR2, (c and lambda_P). We introduce canonically-conjugate variables (chi^0, chi) to (epsilon, pi) of Judes-Visser. Together, they bring in a formal element of linearity and locality in an otherwise non-linear and non-local theory. Special relativities with two invariant scales provide all corrections, say, to the standard model of the high energy physics, in terms of one fundamental constant, lambda_P. It is emphasized that spacetime of special relativities with two invariant scales carries an intrinsic quantum-gravitational character. In an addenda, we also comment on the physical importance of a phase factor that the whole literature on the subject has missed and present a brief critique of SR2. In addition, we remark that the most natural and physically viable SR2 shall require momentum-space and spacetime to be non-commutative with the non-commutativity determined by the spin content and C, P, and T properties of the examined representation space. Therefore, in a physically successful SR2, the notion of spacetime is expected to be deeply intertwined with specific properties of the test particle.Comment: Int. J. Mod. Phys. D (in press). Extended version of a set of two informal lectures given in "La Sapienza" (Rome, May 2001

Twisting kappa-deformed phase space

We briefly discuss the twisting procedure applied to the $\kappa$-deformed space-time. It appears that one can consider only two kinds of such twistings: in space and time directions. For both types of twisitngs we introduce related phase spaces and consider briefly their properties. We discuss in detail the changes of duality relations under the action of twist. The Jordanian twisted space-time and phase space in D=2 are also commented.Comment: LaTeX, 18 pages, revised version, accepted for publication in Journal of Physics

New varying speed of light theories

We review recent work on the possibility of a varying speed of light (VSL). We start by discussing the physical meaning of a varying $c$, dispelling the myth that the constancy of $c$ is a matter of logical consistency. We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a color dependent speed of light; varying $c$ induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation. We show how VSL scenarios may solve the cosmological problems usually tackled by inflation, and also how they may produce a scale-invariant spectrum of Gaussian fluctuations, capable of explaining the WMAP data. We then review the connection between VSL and theories of quantum gravity, showing how ``doubly special'' relativity has emerged as a VSL effective model of quantum space-time, with observational implications for ultra high energy cosmic rays and gamma ray bursts. Some recent work on the physics of ``black'' holes and other compact objects in VSL theories is also described, highlighting phenomena associated with spatial (as opposed to temporal) variations in $c$. Finally we describe the observational status of the theory. The evidence is currently slim -- redshift dependence in the atomic fine structure, anomalies with ultra high energy cosmic rays, and (to a much lesser extent) the acceleration of the universe and the WMAP data. The constraints (e.g. those arising from nucleosynthesis or geological bounds) are tight, but not insurmountable. We conclude with the observational predictions of the theory, and the prospects for its refutation or vindication.Comment: Final versio

Quantum Spacetime Phenomenology

I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. And my main focus is on phenomenological programs that managed to affect the directions taken by studies of quantum-spacetime theories.Comment: 125 pages, LaTex. This V2 is updated and more detailed than the V1, particularly for quantum-spacetime phenomenology. The main text of this V2 is about 25% more than the main text of the V1. Reference list roughly double